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On the [openface C]n/[openface Z]m fractional branes

J. Math. Phys. 50, 022304 (2009); doi:10.1063/1.3072696

Published 23 February 2009

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Robert L. Karp
Department of Physics, Virginia Tech Blacksburg, Virginia 24061, USA
We construct several geometric representatives for the [openface C]n/[openface Z]m fractional branes on either a partially or the completely resolved orbifold. In the process we use large radius and conifold-type monodromies and provide a strong consistency check. In particular, for [openface C]3/[openface Z]5 we give three different sets of geometric representatives. We also find the explicit Seiberg duality which connects our fractional branes to the ones given by the McKay correspondence. ©2009 American Institute of Physics
History: Received 12 April 2008; accepted 16 December 2008; published 23 February 2009
Permalink: http://link.aip.org/link/?JMAPAQ/50/022304/1
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KEYWORDS and PACS

Keywords
PACS
  • 11.25.Uv
    D branes
  • 11.25.Mj
    Compactification and four-dimensional string models
  • YEAR: 2009

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ISSN:
0022-2488 (print)   1089-7658 (online)
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REFERENCES (45)
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  1. M. R. Douglas, J. Math. Phys. 42, 2818 (2001), e-print arXiv:hep-th/0011017.
  2. P. S. Aspinwall and M. R. Douglas, J. High Energy Phys. 0205, 031 (2002), e-print arXiv:hep-th/0110071.
  3. M. R. Douglas and G. W. Moore, “D-branes, quivers, and ALE instantons,” e-print arXiv:hep-th/9603167.
  4. T. Bridgeland, A. King, and M. Reid, J. Am. Math. Soc. 14, 535 (2001), e-print arXiv:math.AG/9908027.
  5. E. Witten, J. High Energy Phys. 9812, 019 (1998), e-print arXiv:hep-th/9810188.
  6. D. -E. Diaconescu and J. Gomis, J. High Energy Phys. 0010, 001 (2000),e-print arXiv:hep-th/9906242.
  7. P. S. Aspinwall, Recent Trends in String Theory (World Scientific, Singapore, 2004), pp. 1–152, e-print arXiv:hep-th/0403166.
  8. R. L. Karp, Commun. Math. Phys. 270, 163 (2006), e-print arXiv:hep-th/0510047.
  9. N. Seiberg and E. Witten, Nucl. Phys. B 426, 19 (1994), e-print arXiv:hep-th/9407087.
  10. P. S. Aspinwall and R. L. Karp, J. High Energy Phys. 0304, 049 (2003), e-print arXiv:hep-th/0211121.
  11. R. L. Karp, D-brane stability, geometric engineering, and monodromy in the derived category, e-print arXiv:hep-th/0512343. e-print arXiv:hep-th/0512343.
  12. T. Bridgeland, J. Algebra 289, 453 (2005), e-print arXiv:math.AG/0502050.
  13. S. Benvenuti S. Franco, A. Hanany, D. Martelli, and J. Sparks, J. High Energy Phys. 0506, 064 (2005), e-print arXiv:hep-th/0411264.
  14. C. P. Herzog and R. L. Karp, J. High Energy Phys. 0602, 061 (2006), e-print arXiv:hep-th/0507175.
  15. P. S. Aspinwall and S. Katz, Commun. Math. Phys. 264, 227 (2006), e-print arXiv:hep-th/0412209.
  16. X. De la Ossa, B. Florea, and H. Skarke, Nucl. Phys. B 644, 170 (2002), e-print arXiv:hep-th/0104254.
  17. D. A. Cox and S. Katz, Mirror Symmetry and Algebraic Geometry, Mathematical Surveys and Monographs Vol. 68 (AMS, Providence, RI, 1999).
  18. E. Witten, Nucl. Phys. B 403, 159 (1993), e-print arXiv:hep-th/9301042.
  19. P. S. Aspinwall, B. R. Greene, and D. R. Morrison, Nucl. Phys. B 416, 414 (1994), e-print arXiv:hep-th/9309097.
  20. D. A. Cox, J. Algeb. Geom. 4, 17 (1995), e-print arXiv:alg-geom/9210008.
  21. W. Fulton, Introduction to Toric Varieties, Annals of Mathematics Studies Vol. 131 (Princeton University Press, Princeton, NJ, 1993).
  22. I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants (Birkhäuser, Boston, MA, 1994).
  23. D. R. Morrison and M. Ronen Plesser, Nucl. Phys. B 440, 279 (1995), e-print arXiv:hep-th/9412236.
  24. R. P. Horja, Duke Math. J. 127, 1 (2005), e-print arXiv:math.AG/0103231.
  25. D. O. Orlov, J. Math. Sci. (N.Y.) 84, 1361 (1997), e-print arXiv:math.AG/9606006.
  26. Y. Kawamata, Am. J. Math. 126, 1057 (2004), e-print arXiv:math.AG/0210439.
  27. P. S. Aspinwall, R. L. Karp, and R. P. Horja, Commun. Math. Phys. 259, 45 (2005), e-print arXiv:hep-th/0209161.
  28. P. Seidel and R. P. Thomas, Duke Math. J. 108, 37 (2001), e-print arXiv:math.AG/0001043.
  29. A. Dimca, Singularities and Topology of Hypersurfaces, Universitext (Springer-Verlag, New York, 1992).
  30. D. Rolfsen, Knots and Links, Mathematics Lecture Series Vol. 7 (Publish or Perish, Houston, TX, 1990) (corrected reprint of the 1976 original).
  31. P. S. Aspinwall, J. Math. Phys. 42, 5534 (2001), e-print arXiv:hep-th/0102198.
  32. A. Canonaco and R. L. Karp, “Derived autoequivalences and a weighted Beilinson resolution,” J. Geom. Phys. (to be published), e-print arXiv:math.AG/0610848.
  33. T. Bridgeland, Bull. London Math. Soc. 31, 25 (1999).
  34. A. N. Rudakov, S. A. Kuleshov, S. K. Zube, D. Yu Nogin, A. I. Bondal, A. L. Gorodentsev, M. M. Gorodentsev, M. M. Kapranov, A. V. Kvichansky, and B. V. Karpov, Helices and Vector Bundles, London Mathematical Society Lecture Note Series Vol. 148 (Cambridge University Press, Cambridge, 1990).
  35. D. Auroux, L. Katzarkov, and D. Orlov, “Mirror symmetry for weighted projective planes and their noncommutative deformations,” e-print arXiv:math.AG/0404281.
  36. W. Barth, C. Peters, A. Van de Ven, and K. Hulek, “Compact complex surfaces,” Ergebnisse der Mathematik Vol. 4, 2nd enlarged ed. (Springer-Verlag, Berlin, 2004).
  37. S. I. Gelfand and Y. I. Manin, Methods of Homological Algebra, Springer Monographs in Mathematics, 2nd ed. (Springer-Verlag, Berlin, 2003).
  38. J. McKay, “Graphs, singularities, and finite groups,” The Santa Cruz Conference on Finite Groups, Proceedings of the Symposia in Pure Mathematics Vol. 37 (AMS, Providence, RI, 1980), pp. 183–186.
  39. M. Kapranov and E. Vasserot, “Kleinian singularities, derived categories and Hall algebras,” Math. Ann. 316, 565 (2000), e-print arXiv:math.AG/9812016.
  40. Y. Ito and H. Nakajima, Topology 39, 1155 (2000).
  41. N. Seiberg, Nucl. Phys. B 435, 129 (1995), e-print arXiv:hep-th/9411149.
  42. D. Berenstein and M. R. Douglas, “Seiberg duality for quiver gauge theories,” e-print arXiv:hep-th/0207027.
  43. S. Katz, T. Pantev, and E. Sharpe, Nucl. Phys. B 673, 263 (2003), e-print arXiv:hep-th/0212218.
  44. Y. Kawamata, J. Math. Sci. Univ. Tokyo 12, 211 (2005), e-print arXiv:math.AG/0311139.
  45. A. Canonaco, Mem. Am. Math. Soc. 183(862) (2006).

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